A stochastic wavelet -based data -driven framework for forecasting uncertain multiscale hydrological and water resources processes

Recently, a stochastic data-driven framework was introduced for forecasting uncertain multiscale hydrological and water resources processes (e.g., streamflow, urban water demand (UWD)) that uses wavelet decomposition of input data to address multiscale change and stochastics to account for input variable selection, parameter, and model output uncertainty (Quilty et al., 2019). The former study considered all sources of uncertainty together. In contrast, this study explores how input variable selection uncertainty and wavelet decomposition impact probabilistic forecasting performance by considering eight variations of this framework that either include/ignore wavelet decomposition and varying levels of uncertainty: 1) none; 2) parameter; 3) parameter and model output; and 4) input variable selection, parameter, and model output. For a daily UWD forecasting case study in Montreal (Canada), substantial improvements in forecasting performance (e.g., 16–30% improvement in the mean interval score) was achieved when input variable selection uncertainty and wavelet decomposition were included within the framework. © 2020 Elsevier Ltd